As shown in FIG. 9, a ball guide 1 is formed to allow a guide block 2 to be movable on a rail 3 in a direction indicated by an arrow A or B. In the guide block 2, a large number of balls 4, which is one example of rolling members, are rolled and circulated in an orderly arranged state. During the rolling and circulation, balls 4 residing within a range of a raceway surface length lt are made to come into contact with a raceway surface 3a of the rail 3 and a raceway surface 2a of the guide block 2 so as to sustain load applied to the guide block 2 from outside.
Roller guides, ball splines, ball bushes and others are also formed to allow rolling members to be rolled and circulated, while there are some elements, such as ball slides and cross roller guides, which do not allow rolling members to circulate therein.
In any of these elements, how a crowning is imparted to both end parts of the raceway surface is so important a factor as to determine all performances including accuracy in running and duration of life (refer to “Study on Accuracy Average Effect on Linear Motion Ball Guides System” by Shigeo SHIMIZU, Journal of Japan Society for Precision Engineering, November 1992).
However, as shown in FIG. 10, a conventional crowning 2b has a crowning length Xr (a length from a crowning start point “o” to a crowning end “a”) and a crowning relief amount λe, and is based on a circular arc 5 whose radius R is decided to make the arc abut on a raceway surface 2a at the crowning start point “o”. The radius R is expressed by a mathematical expression 1 and the circular arc 5 is expressed by a mathematical expression 2.
                    R        =                                            X              r              2                        +                          λ              e              2                                            2            ⁢                                                  ⁢                          λ              e                                                          [                  mathematical          ⁢                                          ⁢          expression          ⁢                                          ⁢          1                ]                                                      x            2                    +                                    (                              y                -                R                            )                        2                          =                  R          2                                    [                  mathematical          ⁢                                          ⁢          expression          ⁢                                          ⁢          2                ]            
The formation of the circular arc 5 faithfully on the expression results in an increase in manufacturing costs. Hence, the circular arc has been actually formed as shown in FIG. 11 wherein, with the circular arc 5 as a base, an edge ranging from the crowning start point “o” to the point “a” decided by the crowning relief amount λe at the crowning end 2c is chamfered linearly, or as shown in FIG. 12 wherein an edge starting from the crowning start point “o” is formed into a polygonal shape whose apexes are points “d”, “c”, “b” and “a” on the circular arc 5.
As shown in FIG. 10, however, in the case of the circular-arc crowning, a crowning relief amount λx, which depends on a distance “x” starting from the crowning start point “o”, becomes large while the distance “x” is still small. As a result, it has been that a ratio of load (load factor) sustained by the balls 4 positioned on the flat raceway surface 2a to load sustained by the balls 4 residing in the range of the crowning length Xr becomes lower.
Additionally, please see “On load rating of a linear motion ball bearing” by Shigeo SHIMIZU, Journal of Japanese Society of Tribologists, November 1999, and “Dynamic capacity of a linear motion rolling guide element” by Shigeo SHIMIZU, Kosaido Co., Ltd., February 1999.